image: Figure 1 | Narwhal-shaped wavefunction. The mode volume characterizes the spatial confinement of an electromagnetic eigenmode and directly determines the strength of light–matter interactions. It is defined as the ratio of the total electric energy density integrated over all space to its peak value. Achieving strong confinement requires designing eigenmodes whose field distributions decay rapidly across space, thereby enhancing the energy density per unit volume. Narwhal-shaped wavefunctions, which combine local power-law enhancement with global exponential decay, enable light to be focused and compressed far beyond conventional limits under lossless conditions.
Credit: Renmin Ma et al.
Photonic devices have long lagged behind electronics in the race to shrink. The reason is fundamental: the uncertainty principle ties light’s spatial confinement to its wavelength, which in the visible and near-infrared can be up to a thousand times larger than the de Broglie wavelength of electrons in circuits. This mismatch has kept photonic chips bulky and placed hard limits on the resolution of optical imaging.
Plasmonics once offered a way around the barrier, using metals to squeeze light into subwavelength volumes. But metals dissipate energy as heat — a trade-off that has blocked progress toward efficient, large-scale integration.
In 2024, a team led by Ren-Min Ma at Peking University, China reported a breakthrough [Nature 632, 287–293 (2024)]. They introduced the singular dispersion equation — a new theoretical framework that shows how light can be confined to extreme scales in lossless dielectric materials. By relying solely on dielectric materials, the approach avoids ohmic loss and paves the way for a new generation of compact, energy-efficient photonic devices.
In a new paper published in eLight, the same team reveals that the extraordinary confinement enabled by the singular dispersion equation arises from a new class of electromagnetic eigenmodes — the so-called narwhal-shaped wavefunctions (Fig. 1). These modes combine local power-law enhancement with global exponential decay, allowing electromagnetic fields to focus and compress far beyond conventional limits.
Building on this insight, the researchers designed and experimentally demonstrated a three-dimensional singular dielectric resonator capable of sub-diffraction confinement in all three spatial dimensions (Fig. 2). Using near-field scanning measurements, they directly observed narwhal-shaped wavefunctions, clearly capturing their power-law growth near the singularity and exponential decay at longer ranges. The experimental data matched theoretical predictions and full 3D simulations, achieving an ultrasmall mode volume of just 5 × 10⁻⁷ λ³.
Exploiting the extreme localization of narwhal-shaped wavefunctions, the team further developed a novel near-field scanning optical microscopy technique — the singular optical microscope (Fig. 3). By exciting the eigenmodes of singular dielectric cavities, this method produces highly localized electromagnetic fields whose resonance shifts sensitively track fine structural variations. The approach delivered an unprecedented spatial resolution of λ/1000, and successfully imaged arbitrary deep-subwavelength patterns such as the letters “PKU” and “SFM.”
The study shows that the singular dispersion equation gives rise to narwhal-shaped wavefunctions — exotic modes that trap light at extreme scales in lossless dielectrics. This discovery underpins what the team calls singulonics: a new nanophotonic paradigm that enables deep-subwavelength confinement and control of light without the penalty of dissipation. The advance could fuel ultra-efficient information processing, open fresh directions in quantum optics, and extend the reach of super-resolution imaging.
Journal
eLight
Article Title
Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging